Differential Kuster-Toksöz Rock Physics Model for Multiple-porosity Rocks

Abstract

Kuster-Toksoz model (KTM) is a classical rock physics model concerning the influence of pore geometry on elastic wave velocities. However, this model is limited to dilute concentration of pores. That is to say, the porosity could not be too high (porosity (Φ)/aspect ratio (α) <<1). In order to solve this problem, this paper transforms the Kuster-Toksoz model into a differential Kuster-Toksoz treatment. In other words, we consider a process whereby porosity, or equivalently inclusions with certain geometries, increases step by step from zero up to its final value. Obviously, this new differential Kuster-Toksoz model (DKTM) is superior to the classical KTM and DEM (short for differential effective medium) model since it considers multiple–porosity and higher porosity rocks. Furthermore, when void pores and clay are considered as inclusions, we analyze the elastic moduli simulated by KTM and DKTM, the geometry parameter of which is described by Berryman’s special pores. The result shows that, DKTM is superior to KTM for obtaining satisfactory elastic properties under high porosity and high volume fraction inclusion condition.